Electric power flow through an alternating current transmission line is a function of the line impedance, the magnitudes of the sending-end and the receiving-end voltages, and the phase angle between such voltages, as shown in FIG. 1. In order to regulate the voltage at any point in a transmission line, an in-phase or an out-of-phase voltage in series with the line is injected. FIG. 2 shows the shunt compensating transformer scheme for voltage regulation in a transmission line. The exciter unit consists of a three-phase Y-connected primary winding, which is impressed with the initial line voltage, v1′ (i.e., v1A′, v1B′, and v1C′). The shunt-compensating unit consists of a total of six secondary windings (two windings in each phase for a bipolar voltage injection). The line is regulated at a voltage, v1 by adding a compensating voltage, v11′, either in- or out-of-phase with the line voltage. The bipolar compensating voltage in any phase is induced in two windings placed on the same phase of the transformer core. To control the shunt compensating unit, a reference voltage V1* is fed to a gate pattern logic which monitors the magnitude V1′ of the exciter voltage, v1′, and determines the number of turns necessary on the shunt compensating unit. Based on this calculation, an appropriate thyristor valve is switched on in a tap changer (FIG. 3), which puts the required number of turns in series with the line.
FIG. 3 shows the schematic diagram of a thyristor-controlled tap changer. A transformer winding is tapped at various places. Each of the tapped points is connected to one side of a back-to-back thyristor (triac) switch. The other sides of all the thyristor switches are connected together at point A. Depending on which thyristor is on, the voltage between points A and B can be varied between zero and the full winding voltage with desired steps in between. In a mechanical version of this arrangement, a load tap changer connects with one of a number of taps to give a variable number of turns between the connected tap and one end of the winding.
The effective angle of a transmission line is varied by using a Phase Shifting Transformer, which is also known as a Phase Angle Regulator (PAR). A PAR injects a voltage in series with the transmission line and in quadrature with the phase-to-neutral voltage of the transmission line as shown in FIG. 4A. The series injected voltage introduces a phase shift whose magnitude in radians varies with the magnitude of the series-injected voltage input where the phase-to-neutral voltage of the transmission line is the base voltage. In a typical configuration, a PAR consists of two transformers (FIG. 4B). The first transformer in the exciter unit is a regulating transformer that is shunt connected with the line. The first, regulating transformer primary windings are excited from the line voltage and a voltage is induced in the secondary windings. A voltage with variable magnitude and in quadrature with the line voltage is generated from the phase-to-phase voltage of the induced voltage of the first transformer using taps. For series injection of this voltage, an electrical isolation is necessary.
The second transformer in the series unit is a series transformer that is excited from the phase-to-phase voltage of the regulating transformer and its induced voltage is connected in series with the line. Since the series injection voltage is only a few percent of the line voltage, the series transformer can be a step-down transformer. The primary winding of the series transformer as well as the secondary winding of the regulating transformer can be high voltage and low current rated so that the taps can operate normally at low current and can ride through high fault current.
The impedance of the transmission line is typically inductive; accordingly, power flow can be decreased by inserting an additional inductive reactance in series with the transmission line, thereby increasing the effective reactance of the transmission line between its two ends. The power flow can also be increased by inserting an additional capacitive reactance in series with the transmission line, thereby decreasing the effective reactance of the transmission line between its two ends. The indirect way to emulate an inductive or a capacitive reactance is to inject a voltage in quadrature with the prevailing line current by using a Voltage Source Converter.
The characteristics of mechanically switched and Thyristor-controlled Power Flow Controllers are such that each controller can control only one of the three transmission parameters (voltage, impedance, and angle). Therefore, changing one parameter affects both the real and the reactive power flow in the transmission line.
The desired operation of an ideal power flow controller is described below. FIG. 5(a) shows a single line diagram of a simple transmission line with an inductive reactance, XL, and a series insertion voltage, Vdq, connecting a sending-end voltage source, Vs, and a receiving-end voltage source, Vr, respectively. The voltage across the transmission line reactance, XL, is VX=Vs−Vr−Vdq=I XL where I is the current in the transmission line. Changing the insertion voltage, Vdq, in series with the transmission line can change the voltage, VX, across the transmission line and, consequently, the line current and the power flow in the line will change.
Consider the case where Vdq=0 (FIG. 5(b)). The transmission line sending-end voltage, Vs, leads the receiving-end voltage, Vr, by an angle δ. The resulting current in the line is I; the real and the reactive power flow at the receiving end are P and Q, respectively. With an injection of Vdq in series with the transmission line, the transmission line sending-end voltage, Vo still leads the receiving-end voltage, Vr, but by a different angle δ1 (FIG. 5(c)). The resulting line current and power flow change, as shown. With a larger amount of Vdq injected in series with the transmission line, the transmission line sending-end voltage, Vo, now lags the receiving-end voltage, Vr, by an angle δ2 (FIG. 5(d)). The resulting line current and the power flow now reverse. Notice that the injected series voltage, Vdq, is at any angle, Φ, with respect to the line current, I.
For a desired amount of real and reactive power flow in a line, the magnitude and the angle of the series injected voltage are varied. The compensating voltage, being at any angle with the prevailing line current, emulates in series with the transmission line a capacitor that increases the power flow in the line, an inductor that decreases the power flow in the line, a positive resistor that absorbs real power from the line and a negative resistor that delivers real power to the line.
Referring now to FIG. 6, a Versatile Power Flow Transformer (VPFT) is shown for implementing power flow control in a transmission line of a power transmission system. As shown, in the VPFT, the line voltage is applied across the primary windings 1A, 1B, 1C in the exciter unit (only winding 1A being shown). Each primary winding has three secondary windings in series, for a total of nine secondary windings—a1, c2 and b3 on the core of A-phase; b1, a2 and c3 on the core of B-phase; and c1, b2 and a3 on the core of C-phase. As seen, a compensating voltage for any phase is derived from the vectorial sum of the voltages induced in a three-phase winding set—a1, a2 and a3 for injection in A-phase; b1, b2 and b3 for injection in B-phase; and c1, c2 and c3 for injection in C-phase. Importantly, a tap is employed on each of the nine secondary windings so that each entity in each vectorial sum can be individually magnitudally varied. Each tap may be a mechanical or solid-state tap changer such as the tap changer of FIG. 3, e.g., although other types of taps may be employed.
For example, and more specifically, the voltage V21A (shown) is the sum of at least a tapped portion of the voltage across a1 as derived from A-phase, at least a tapped portion of the voltage across a2 as derived from B-phase, and at least a tapped portion of the voltage across a3 as derived from C-phase:V21A=% x a1+% y a2+% z a3;and voltage V21A is injected as a compensating voltage in line with V1A to produce compensated voltage V2A: V2A=V21A+V1A.Compensating voltages V21B for the B-phase and V21C for the C-phase are similarly produced:V21B=% x b1+% y b2+% z b3;V2B=V21B+V1B.V21C=% x c1+% y c2+% z c3;V2C=V21C+V1C.Notably, a1, b1, and c1 should be substantially identical; a2, b2, and c2 should be substantially identical; and a3, b3, and c3 should be substantially identical. In addition, each of % x, % y, and % z should be substantially identical across the phases of the VPFT. Accordingly, the magnitude of the produced V21A, V21B, and V21C should be substantially identical; and V21A, V21B, and V21C should be substantially 120 degrees out of phase with each other, assuming that V1A, V1B, and V1C are substantially 120 degrees out of phase with each other. Accordingly, the transmission lines A, B, and C as compensated are substantially in balance.
FIG. 7 shows a control block diagram of a controller for controlling the series impedance emulation achieved by the VPFT of FIG. 6. The steps performed by such controller are as follows. An instantaneous 3-phase set of line voltages, v1, (i.e., v1A, v1B, v1C) is used to calculate the reference angle, Θ, which is phase-locked to the phase a of the line voltage, v1A. From an instantaneous 3-phase set of measured line currents, i, the magnitude, I, and its relative angle, Θir, with respect to the phase-lock-loop angle, Θ, are calculated. From the compensating resistance demand, R*, and the compensating reactance demand, X*, both externally supplied, the demanded impedance's magnitude, Z*, and angle, Θz, are calculated. The magnitude, I, of the line current multiplied by the compensating impedance demand, Z*, is the insertion voltage magnitude demand, Vdq*. The relative phase angle, β, of this insertion voltage demand is Θir+Θz.
Once the desired series injection voltage, Vdq*, and its angle, β, are defined, the Tap Control Unit in FIG. 15 determines the contribution from each winding of a 3-phase set (a1, a2, and a3 for injection in A-phase; b1, b2, and b3 for injection in B-phase; and c1, c2, and c3 for injection in C-phase) to constitute Vdq* in particular, from knowledge of the magnitude of the exciter voltage, V1, the Tap Control Unit determines the number of turns necessary on each winding of the series-compensating unit. Based on this calculation, the appropriate taps are switched on via an appropriate mechanical or solid state tap changer (see FIG. 3, e.g.), which accordingly put the required number of turns in series with the line. In addition, a VPFT can regulate the line voltage by utilizing the unused portions of the transformer windings as a shunt compensating unit.
FIG. 8 shows a model of the basic VPFT of FIG. 6 as coupled to a simple power transmission system, and also a phasor diagram of the transmission system. As seen, in the system the sending-end voltage is Vs, the receiving-end voltage is Vr, the voltage across the line impedance XL, is VX, and the inserted voltage is Vdq, and has a controllable magnitude (0≦Vdq≦Vdqmax) and angle (0≦ρ≦360°). The inserted voltage Vdq is added to the fixed sending-end voltage, Vs, to produce the effective sending-end voltage, Vo=Vs+Vdq. The difference, Vo−Vr, provides the compensated voltage, VX, across XL. As angle ρ is varied over its full 360° range, the end of phasor Vdq moves along a circle with its center located at the end of phasor Vs. The rotation of phasor Vdq with angle ρ modulates both the magnitude and the angle of phasor VX and, therefore, both the transmitted real power, P, and the reactive power, Q, vary with ρ in a sinusoidal manner.
This process, of course, requires the compensating voltage, Vdq, to supply and absorb both real and reactive power, Pexch and Qexch, which are also sinusoidal functions of angle ρ, as shown in FIG. 8. The exchanged real power, Pexch, and reactive power, Qexch, by the injected voltage source with the line are:Pexch=Vdq*I=Vdq I cos φ=Vd I, andQdq=Vdq×I=Vdq I sin φ=Vq I.
The exchanged real and reactive power, Pexch and Qexch, must flow through another source or sink. Since the compensating voltage is derived from the line voltage through a transformer action with the primary winding, the exchanged real and reactive power with the line must flow through the primary winding to the line. Since the series injected voltage is, typically, only a few percent of the line voltage, the shunt current would be the same few percent of the line current. The current through the exciter unit has both real and reactive components. The loading effect of these two currents on the power system network is independent of each other as shown.
In an alternate method of emulating in series with a transmission line for selective real and reactive flow in the line, a Voltage Source Converter (VSC)—based Unified Power Flow Controller (UPFC) is employed. A UPFC injects, in series with the line, a variable magnitude and variable angle voltage, thereby exchanging both real and reactive power with the line. The difference between a UPFC and a VPFT is that in a UPFC, only the exchanged real power flows back and forth through the shunt unit to the line.
Significantly, the methods and apparatus set forth above are related to power flow control in a single transmission line to which a controller is connected. However, in transmission systems in general, transmission lines are usually connected at common voltage buses. Therefore, any change in power flow in one line will affect the power flow in other lines as well. Thus, the real power burden cannot be directly transferred from one specific line to another.
Turning now to FIG. 9, it is seen that an Interline Power Flow Controller (IPFC) generally has a number of VSCs, where each VSC is connected in series with a particular transmission line through a coupling transformer. Each VSC has a set of DC terminals, and all the VSCs in the IPFC are connected at their common DC terminals. The voltage injected in series with each line by a respective VSC has a direct or real component and a quadrature or reactive component with respect to the prevailing line current. The quadrature component provides capacitive or inductive compensation that increases or decreases the power flow of the specific line. The real component results in an exchange of real power with the specific line. The real power can be transferred from one line to another through a common DC link capacitor (not shown). The IPFC can thus equalize both real and reactive power flow between transmission lines by transferring real power from over-loaded to under-loaded lines. However, and importantly, using the IFPC for this purpose is relatively expensive.
A VSC is capable of injecting a voltage into a transmission line, although it is known that doing so in sub-cycle time is not advisable. In particular, if the series injection transformer of a VSC is not properly rated, a sudden injection of voltage may cause transformer saturation, and system instability may occur. Also, a VSC is not preferred since the output voltage of a VSC always injects harmonic components into the power system network.
As is known, a VSC unit is essentially an AC voltage source behind the leakage reactance of the coupling transformer. Since the coupling transformer and other magnetic circuits offer an inherent leakage reactance, there is a corresponding inductive compensation, whether desired or not, before the VSC even provides any compensation. For example, a converter rated for 1 pu capacitive and 1 pu inductive compensation with a 15% leakage reactance actually provides 0.85 pu capacitive and 1.15 pu inductive compensation to the transmission line. As should be appreciated, then, a VSC is not dependable to be used to limit a fault current.
To limit the fault current to the fullest extent, then, the VSC has to be operational without providing any reactance compensation so that the VSC may be able to emulate the highest possible inductor that its rating permits. In another extreme case, consider the VSC is providing the fullest possible inductive compensation in series with the line before a fault occurs, in which case the VSC is providing a series injection of rated voltage while carrying a rated current. In the event of a fault, the current through the VSC rises and the compensator has to be bypassed; otherwise the converter will be destroyed from the increasing fault current.
A need exists, then, for a method and apparatus for transferring power from an over-loaded transmission line to an under-loaded transmission line in a multi-line transmission system with minimum impact on power flow in other lines in the transmission system. More particularly, a need exists for such a method and apparatus which generates the required compensating voltage of line frequency directly by using reliable, traditional and thus less expensive technology, which does not generate any extra harmonic component.